Let me start with a caveat, “inter se”
movement between currencies and the premia or discount that one currency
commands over another currency, over a period depend on various factors. Just
to list a few,
a) the
respective Interest rates in each currency ,
b) short term availability and requirement of
the currencies,
c) Balance of payments of trade movement in
the short term between two countries ,and of course the most important ,
d) Government regulations and restrictions
imposed on the currency
e) Intervention by the Government in
buying/selling of the currencies
f) Speculative play by private players
Discussion here would be on incremental
inter se movements between currencies and not on the base rate itself. The base
currency rate between two or more currencies depend on factors starting from
Purchase power parity, Balance of payments of trade as of a certain date and
various other factors including
historical,which is possibly a subject for discussion for another day.
Just to make it doubly clear this piece is
only on movement of Forex rates between currencies and the way forward premia
/discount gets fixed between the currencies. For the sake of simplicity, we will
take USD and INR with which people are generally familiar.
One compelling theory and what could be
termed as a classical one on forex movement is the one with reference to “Interest
rate differential between currencies”. This is the simplest, most logical and
something which should work if the market is perfect and there are no
restrictions on currency movement, investment or borrowing in the currencies
under study.
What
is “Interest rate differential theory”?
First let us define what is interest rate? People understand that
interest rate is the rate an investment fetches in a certain currency. A
deposit in India in Indian rupee fetches anything between 5-10% depending on
the period of deposit etc. Similarly a deposit in USD in US would fetch
something in the region of 2%-4%. We all broadly know that Interest is a
function of the underlying inflation of the country’s economy and the real
return expectations.
The comparable difference between
interests can be termed “Interest rate differential”.
Let us start off with a base rate of 1 USD
= INR 55. To make understanding easy, let us also assume that the interest in
USD is 2% and interest in INR is 8%. $ 1 deposit would at the end of one year be
equal to $ 1.02 and a Rs. 55 deposited for one year would be Rs. 55*1.08=Rs
59.40. In an ideal situation, USD 1.02 should equal Rs. 59.40 that is 1 USD
should be Rs. 59.4/1.02 ,that is, Rs. 58.24 one year from now. The one year
forward premia on USD ,which fetches you
Rs. 55 immediately and where the interest rate differential is 6% (8%-2%)
should be Rs 3.24 ,(58.24-55.00) to a USD. If this is not the case, there would
be a situation of what is termed “arbitrage” or opportunities to make riskless
profit. Let us see it can happen.
Let us do a simple one between USD and
INR. Let us take the numbers from the same example. For the sake of simplicity
we will have to assume no interest rate differential between borrowing and
Investing .This is to make the example easier.
Normally the currency on which interest
rate is lower will be at a premium and the one whose interest rate is higher
will be at a discount.
Let us assume that at the interest levels
specified, the actual forward rate quoted at the end of one year is at INR 55
to a USD, that is there is no premia or discount.
Easy way to make profit is
- borrow in USD,
- convert to INR immediately,
- deposit in INR,
- simultaneously take a forward cover to
buy USD at INR 55.
Let us calculate the flows.
Since you have borrowed in USD, you will
have to pay $ 1.02 with interest at the end of one year.
USD converted to INR 55 and deposited
would become INR 59.40 at the end of one year since INR deposit attracts 8 %
interest.
Since a forward cover has been taken, you
would be in a position to buy USD of 1.02 for a total outflow of INR 1.02*55=Rs.
56.10.This leaves you Rs 59.40-Rs 56.10=Rs3.30 as riskless profit.
In the same case, if at the same interest
rates, INR one year forward rate had been INR 62 to USD, we will be doing the borrowing in
INR, depositing in USD, take one year forward cover to sell USD
Let us work out the simple math in this
sequence.
You had borrowed INR 55 for a year, to be
returned after a year would be Rs 55*1.08=59.40
INR borrowed was converted to 1 USD at the
beginning has been deposited as USD deposit .At the end of one year we get USD
1.02.
Since we had a cover to sell USD at the
rate of INR 62 to a USD, we will sell the $ 1.02 at INR 62 to a USD and get on
hand INR 1.02*62 =63.24 at the end of one year.
At the end of one year, we can pay off the
INR borrowings of Rs 55 with interest, Rs.59.40
and would be left with INR 63.24-59.40=Rs.3.84 as riskless profit.
Through this iteration, one will find that forward premia of Rs 3.24 to a USD is the equilibria
rate.
We have assumed no difference in interest
rates between borrowing and investing and also no difference between buying and
selling of currency. Margins between these two will make a slight difference in
the calculations but the theory holds good.
As a thumb rule, arbitrage opportunity
will arise when the currency forward rate is different from the interest rate
differential. Normally in such situations the demand/supply for the currencies
adjusts in such a way that the interest rates move and nullify the advantage.
If this kind of anomaly were to persist, everyone will be doing this set of
transaction and the interest rates and the demand for the currency will
drastically undergo a change till such time equilibrium is attained.
This is a theory, a sound one at that but will continue to be theory till such time , we
have free currency movements and unrestricted deposit and borrowings in any
currency in any country or at least in the countries of the currencies in
question/discussion.It has its practical limitations in the current economic
milieu but can be very useful pointer for course corrections and to see through
huge anamolies.
This piece was posted in CAClub website by the undersigned a few weeks back.
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